Questions

I am looking to develop a prototype of an electronic gadget and ready with the design specifications. Have a few questions to people who have successfully got their products manufactured in China.
How do I go about looking for companies in China that can develop the prototype for me?
How much does it cost to develop a prototype vis a vis actual product cost at scale (say 1000 pieces)
How is my IP protected?

There are a number of different questions here, so I'll try to answer what I think you're really asking.

My background is in electronic product development in a corporate B2B environment, so the question of 'Should I go to China' almost invariably comes up in conversation.

My first question would really be: Why China? What appeals to you about developing / manufacturing in China over the country where you live? Is it just cost?

There are a few general things to note:
1) Manufacturing (note: manufacturing) in China CAN be cheaper than first world countries like the USA or UK, but this is not always the case.
For one thing, Chinese manufacturers will produce EXACTLY what you ask them to make. If something is wrong with YOUR design, it'll be included in the final product. Few will make adjustments to correct anything that's wrong (I'm not sure if they just don't care, or it's a general philosophy, but it's what I've seen). Western manufacturers are much more vocal about identifying any issues for rectification before proceeding. Not all, but more than in China. Basically this means that if your design isn't perfect the first time around, you are going to end up with wastage in the manufacturing process. Hardware is something you don't want to be doing through 'trial and error', so make sure your manufacturing processes are spot on before going to China.

From a design perspective, product development is a highly interactive experience, especially if you are engaging with an external team (such as a Chinese one). Therefore whoever you engage with need to have EXCEPTIONAL communication skills, both in language and general ability to communicate with you. If they don't, the process is going to take months, if not years longer than it needs to, and cost a lot more as well (even if labour rates are much lower in China for equivalent talent).

I realise I haven't put a concrete value around how much it will cost, but as anyone in product development will tell you: It depends. Without having an understanding of what exactly your electronic device is, there is no way to put a number to it. I've seen simple developments start at $20k for a prototype, all the way through to $500k for a fully fledged intrinsically safe camera system. That's in US dollars, but China won't necessary be that much cheaper, ESPECIALLY if you have to fly over there for meetings with designers, manufacturers, do multiple re-spins of everything due to communication errors, etc.

2) In terms of IP, China is definitely getting better than what it was, but it's worth noting that you have to be very very clear about IP with manufacturers. You have to explicitly state in contracts that they are not allowed to make copies for their own use or sale. What is being manufactured on their line is yours, and yours alone. As the advice always is when it comes to stuff like this, talk to a lawyer.

It's also worth finding companies who have engaged with Chinese manufacturing before, to see who they've used and how they found the experience. We've been involved with In-Tech Electronics (HQ in Hong Kong, factory in Shenzhen, and speak a lot of English, which helps), and they've been very good. Some of our larger clients have also used them previously.